How to texture paint one image over another image, while still keeping the background color of the first image
One way to do this is to prepare your sheet music image with a transparent background. Select the black notes and text and invert the selection and remove the white background. Export this as .png.
In Blender, UV Editing mode create a new image and unwrap your object. After unwrapping and before texture painting, create two new textures in Texture Properties tab, one with your base of old paper and another texture with your notes on a transparent background.
In Texture Paint mode, paint the base coat, then switch the texture to your notes and text, and paint over the base coat. Save the Image, and then apply it as an image texture into the Base Color of the Principled BSDF.
Hope that helps, I think mixing the images in this case will want to produce a slightly washed out mix of the old paper with the bright white of the sheet music. But give that a try and see if you like that result better.